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Epidemic outbreaks and the optimal lockdown area: a spatial normative approach

Author

Listed:
  • Davide Torre

    (SKEMA Business School and Universite Cote d’Azur, Sophia Antipolis)

  • Danilo Liuzzi

    (University of Milan)

  • Simone Marsiglio

    (University of Pisa)

Abstract

Infectious diseases generate heterogeneous economic and health impacts within countries, thus it is essential to account for the spatial dimension in the design of epidemic management programs. We analyze the optimal regional policy to contain the spread of a communicable disease in a spatial framework with endogenous determination of the regional borders characterizing which policy regime will prevail. Specifically, the social planner needs to choose how to split the entire spatial economy in a number of regions in which a different combination of lockdown and treatment measures will be employed: in some region the only mitigation instrument will be treatment, while in some other treatment will be accompanied by a partial lockdown. We characterize the optimal solution both in an early and an advanced epidemic setting, showing that according to the circumstances it may be convenient either to partition the spatial economy in multiple regions with differentiated policies or to consider it a unique region subject to the same policy measure. Moreover, we show that from a normative perspective it is rather difficult to understand how to effectively determine the optimal size of a lockdown area (and thus of the lockdown intensity) since this critically depends on a number of factors, including the initial spatial distribution of disease prevalence, the amount of resources diverted from one region to the other, and the possible spatio-temporal evolution of the disease.

Suggested Citation

  • Davide Torre & Danilo Liuzzi & Simone Marsiglio, 2024. "Epidemic outbreaks and the optimal lockdown area: a spatial normative approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(1), pages 349-411, February.
  • Handle: RePEc:spr:joecth:v:77:y:2024:i:1:d:10.1007_s00199-023-01517-w
    DOI: 10.1007/s00199-023-01517-w
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    1. Boucekkine, R. & Camacho, C. & Fabbri, G., 2013. "Spatial dynamics and convergence: The spatial AK model," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2719-2736.
    2. La Torre, Davide & Malik, Tufail & Marsiglio, Simone, 2020. "Optimal control of prevention and treatment in a basic macroeconomic–epidemiological model," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 100-108.
    3. Boucekkine, Raouf & Camacho, Carmen & Zou, Benteng, 2009. "Bridging The Gap Between Growth Theory And The New Economic Geography: The Spatial Ramsey Model," Macroeconomic Dynamics, Cambridge University Press, vol. 13(1), pages 20-45, February.
    4. La Torre, Davide & Liuzzi, Danilo & Marsiglio, Simone, 2015. "Pollution diffusion and abatement activities across space and over time," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 48-63.
    5. Jérôme Adda, 2016. "Economic Activity and the Spread of Viral Diseases: Evidence from High Frequency Data," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(2), pages 891-941.
    6. Martin S Eichenbaum & Sergio Rebelo & Mathias Trabandt, 2021. "The Macroeconomics of Epidemics [Economic activity and the spread of viral diseases: Evidence from high frequency data]," The Review of Financial Studies, Society for Financial Studies, vol. 34(11), pages 5149-5187.
    7. Pablo D. Fajgelbaum & Amit Khandelwal & Wookun Kim & Cristiano Mantovani & Edouard Schaal, 2021. "Optimal Lockdown in a Commuting Network," American Economic Review: Insights, American Economic Association, vol. 3(4), pages 503-522, December.
    8. Goenka, Aditya & Liu, Lin & Nguyen, Manh-Hung, 2014. "Infectious diseases and economic growth," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 34-53.
    9. Mariko J. Klasing & Petros Milionis, 2020. "The international epidemiological transition and the education gender gap," Journal of Economic Growth, Springer, vol. 25(1), pages 37-86, March.
    10. Philipson, Tomas, 2000. "Economic epidemiology and infectious diseases," Handbook of Health Economics, in: A. J. Culyer & J. P. Newhouse (ed.), Handbook of Health Economics, edition 1, volume 1, chapter 33, pages 1761-1799, Elsevier.
    11. Wang, Tao, 2014. "Dynamics of an epidemic model with spatial diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 119-129.
    12. Camacho, Carmen & Zou, Benteng & Briani, Maya, 2008. "On the dynamics of capital accumulation across space," European Journal of Operational Research, Elsevier, vol. 186(2), pages 451-465, April.
    13. La Torre, Davide & Liuzzi, Danilo & Marsiglio, Simone, 2019. "Population and geography do matter for sustainable development," Environment and Development Economics, Cambridge University Press, vol. 24(2), pages 201-223, April.
    14. John R. Birge & Ozan Candogan & Yiding Feng, 2022. "Controlling Epidemic Spread: Reducing Economic Losses with Targeted Closures," Management Science, INFORMS, vol. 68(5), pages 3175-3195, May.
    15. Bloom, David E. & Canning, David & Sevilla, Jaypee, 2004. "The Effect of Health on Economic Growth: A Production Function Approach," World Development, Elsevier, vol. 32(1), pages 1-13, January.
    16. Goldman Steven Marc & Lightwood James, 2002. "Cost Optimization in the SIS Model of Infectious Disease with Treatment," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 2(1), pages 1-24, April.
    17. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2019. "Growth and agglomeration in the heterogeneous space: a generalized AK approach," Journal of Economic Geography, Oxford University Press, vol. 19(6), pages 1287-1318.
    18. Raouf Boucekkine & Rodolphe Desbordes & Hélène Latzer, 2009. "How do epidemics induce behavioral changes?," Journal of Economic Growth, Springer, vol. 14(3), pages 233-264, September.
    19. Mark Gersovitz & Jeffrey S. Hammer, 2004. "The Economical Control of Infectious Diseases," Economic Journal, Royal Economic Society, vol. 114(492), pages 1-27, January.
    20. Torre, Davide La & Liuzzi, Danilo & Marsiglio, Simone, 2021. "Transboundary pollution externalities: Think globally, act locally?," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    21. de Frutos, Javier & Martín-Herrán, Guiomar, 2019. "Spatial vs. non-spatial transboundary pollution control in a class of cooperative and non-cooperative dynamic games," European Journal of Operational Research, Elsevier, vol. 276(1), pages 379-394.
    22. Mounir Amdaoud & Giuseppe Arcuri & Nadine Levratto, 2021. "Are regions equal in adversity? A spatial analysis of spread and dynamics of COVID-19 in Europe," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 22(4), pages 629-642, June.
    23. Aditya Goenka & Lin Liu, 2020. "Infectious diseases, human capital and economic growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(1), pages 1-47, July.
    24. Hoyt Bleakley, 2007. "Disease and Development: Evidence from Hookworm Eradication in the American South," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(1), pages 73-117.
    25. Daron Acemoglu & Simon Johnson, 2007. "Disease and Development: The Effect of Life Expectancy on Economic Growth," Journal of Political Economy, University of Chicago Press, vol. 115(6), pages 925-985, December.
    26. de Frutos, Javier & Martín-Herrán, Guiomar, 2019. "Spatial effects and strategic behavior in a multiregional transboundary pollution dynamic game," Journal of Environmental Economics and Management, Elsevier, vol. 97(C), pages 182-207.
    27. La Torre, Davide & Liuzzi, Danilo & Marsiglio, Simone, 2021. "Epidemics and macroeconomic outcomes: Social distancing intensity and duration," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    28. Brock, William & Xepapadeas, Anastasios, 2010. "Pattern formation, spatial externalities and regulation in coupled economic-ecological systems," Journal of Environmental Economics and Management, Elsevier, vol. 59(2), pages 149-164, March.
    29. Mark Gersovitz & Jeffrey S. Hammer, 2003. "Infectious Diseases, Public Policy, and the Marriage of Economics and Epidemiology," The World Bank Research Observer, World Bank, vol. 18(2), pages 129-157.
    30. Eduardo Casas & Christopher Ryll & Fredi Tröltzsch, 2018. "Optimal control of a class of reaction–diffusion systems," Computational Optimization and Applications, Springer, vol. 70(3), pages 677-707, July.
    31. Matteo Cervellati & Uwe Sunde & Simona Valmori, 2017. "Pathogens, Weather Shocks and Civil Conflicts," Economic Journal, Royal Economic Society, vol. 127(607), pages 2581-2616, December.
    32. Davide La Torre & Danilo Liuzzi & Simone Marsiglio, 2022. "Geographical heterogeneities and externalities in an epidemiological‐macroeconomic framework," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(5), pages 1154-1181, October.
    33. Matteo Cervellati & Uwe Sunde & Simona Valmori, 2017. "Pathogens, Weather Shocks and Civil Conflicts," Economic Journal, Royal Economic Society, vol. 127(607), pages 2581-2616, December.
    34. Sebastien Bourdin & Ludovic Jeanne & Fabien Nadou & Gabriel Noiret, 2021. "Does lockdown work? A spatial analysis of the spread and concentration of Covid-19 in Italy," Regional Studies, Taylor & Francis Journals, vol. 55(7), pages 1182-1193, July.
    35. Aditya Goenka & Lin Liu, 2012. "Infectious diseases and endogenous fluctuations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(1), pages 125-149, May.
    36. Brock, William & Xepapadeas, Anastasios, 2008. "Diffusion-induced instability and pattern formation in infinite horizon recursive optimal control," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 2745-2787, September.
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    1. Raouf Boucekkine & Ted Loch-Temzelides, 2024. "Introduction to the special issue on mathematical economic epidemiology models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(1), pages 1-7, February.
    2. Taojie Qin & Xianghua Gan & Yuchen Li & Changsheng Qin, 2024. "Optimizing Cross-Regional Lockdown Policies for Epidemics: Balancing Economic and Public Health Costs," Sustainability, MDPI, vol. 16(17), pages 1-14, September.

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    More about this item

    Keywords

    Macroeconomic-epidemiological model; Optimal lockdown area; Regional policy; Spatio-temporal dynamics;
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    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • E20 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - General (includes Measurement and Data)
    • I10 - Health, Education, and Welfare - - Health - - - General

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